With great trepidation, I will add a few things(because of the great internet "more is less principle" :the more there is to read, the less likely you will be able to make sense out of it)

Well begun is half done: Count out the actual length of the melody that you are learning, in measures, and mark out the measures either on a music staff, or with slash marks on a blank page.Something like this would be fine:/----/----/----/----/----/----/ etc

Instead of playing the whole chords, try this--

just find the bass notes by sloshing up and down on the Low E and A strings till you figure out what key you are in (it will generally be the note that you can play most often during the tune, especially in the first and the last measures)

Go back to the beginning, and count measures that you can play this note in *Don"t worry about majors and minors yet*

Mark the only the counts in each the measures that you can play the note on--for a simple blues, it might look like this:

/AAAA/AAAA/AAAA/AAAA/----/----/AAAA/AAAA/----/----/AAAA/----/

Now, instead of having 12 measures to figure out, you only have five. And since you are working with a folk song, in a major key, there are only two other chords, or notes, that you can choose from. A Piece of cake.

The trick is to get the measures that are easy out of the way, and, at the same time, reduce the number of choices for the measures that are hard to figure out. After you've got the bass note for each chord, you will know what the chord should be, and you can figure out major,minor or whatever, very easily.

The way that people get lost is through fudging, since when you fudge, you don't know exactly what you've got and what you don't have.

Other helpful things to remember are:

Chord changes usually come only on the first and third beats of any given measure(and sometimes not that often)

Most songs start and end on the same chord.

Most melodies consist of phrases that are either two or four measures long--

Most songs alternate of a phrase that uses the Tonic(Keyname chord) such as "C" with the dominant "G7"

Although there are many songs, there are fewer melodies, and even fewer still chord progressions, so most songs in a given genre will use one of four or five basic chord progressions, with minor alterations.

Don't let key changes fool you, the chord progression doesn't change.

Every note in a scale is occurs in either the Tonic (C) the Sub-Dominant (F) or the Dominant (G7) chord. That is why most songs end up being three chord tunes.

A lot of minor chords in major melodies (and major chords in minor melodies) are substituted for more basic chords because they add harmonic flavor (which means you don't need them, but it might not sound quite as nice without them)

Figuring out chords progressions isn't so much a matter of figuring out chords, as of recognizing what progression that you are hearing.

My guitar teacher used to get a lot of calls for pick-up up bands, so he decided to learn every tune in the standard fake book (about 1500). He said, after I learned the first fifty, the rest were easy.